发布求助
文献互助 智能选刊 最新文献

Bulletin of the Karaganda University-Mathematics最新文献

筛选
英文 中文
Extensions of some differential inequalities for fractional integro-differential equations via upper and lower solutions 分数阶积分微分方程的一些微分不等式的上下解扩展
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2023-03-30 DOI: 10.31489/2023m1/156-167
A. Yakar, H. Kutlay
{"title":"Extensions of some differential inequalities for fractional integro-differential equations via upper and lower solutions","authors":"A. Yakar, H. Kutlay","doi":"10.31489/2023m1/156-167","DOIUrl":"https://doi.org/10.31489/2023m1/156-167","url":null,"abstract":"This paper deals with some differential inequalities for generalized fractional integro-differential equations by using the technique of upper and lower solutions. The fractional differential operator is taken in Caputo’s sense and the nonlinear term divided into two parts depends on the fractional integrals of an unknown function with two different fractional orders. The results are studied by employing a variety of coupled upper and lower solutions. These theorems have some potential for extending the iterative techniques to fractional order integro-differential equations and to coupled systems of integro-differential fractional equations to obtain the existence of solutions as well as approximate solutions for the considered problem.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45547319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the non-uniqueness of the solution to a boundary value problem of heat conduction with a load in the form of a fractional derivative 带负荷热传导边值问题分数阶导数解的非唯一性
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-12-30 DOI: 10.31489/2022m4/98-106
M. Kosmakova, K.A. Izhanova, A.N. Khamzeyeva
{"title":"On the non-uniqueness of the solution to a boundary value problem of heat conduction with a load in the form of a fractional derivative","authors":"M. Kosmakova, K.A. Izhanova, A.N. Khamzeyeva","doi":"10.31489/2022m4/98-106","DOIUrl":"https://doi.org/10.31489/2022m4/98-106","url":null,"abstract":"The paper deals with the second boundary value problem for the loaded heat equation in the first quadrant. The loaded term contains a fractional derivative in the Caputo sense of an order α, 2<α<3. The boundary value problem is reduced to an integro-differential equation with a difference kernel by inverting the differential part. It is proved that a homogeneous integro-differential equation has at least one non-zero solution. It is shown that the solution of the homogeneous boundary value problem corresponding to the original boundary value problem is not unique, and the load acts as a strong perturbation of the boundary value problem.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47629206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Analytical and numerical research based on one modified refined bending theory 基于一种修正的精细化弯曲理论的分析与数值研究
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-12-30 DOI: 10.31489/2022m4/76-85
A. Kasimov, G. Yessenbayeva, B. Kasimov, O. Khabidolda
{"title":"Analytical and numerical research based on one modified refined bending theory","authors":"A. Kasimov, G. Yessenbayeva, B. Kasimov, O. Khabidolda","doi":"10.31489/2022m4/76-85","DOIUrl":"https://doi.org/10.31489/2022m4/76-85","url":null,"abstract":"In the article, an analytical and numerical study based on one modified refined bending theory is presented. By the finite difference method, a general numerical calculation algorithm is developed. The solution obtained by the proposed method is compared with the results of known solutions, namely, with the solution of the classical theory, the exact solution, the solution in trigonometric series, as well as with experimental data. Comparison of the results obtained by the method given in the article with the solutions determined by other methods shows sufficient accuracy, which indicates the reliability of the proposed method based on one option of the modified refined bending theory. Classical theory is not applicable to such problems under consideration.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46896665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existentially prime Jonsson quasivarieties and their Jonsson spectra 存在素数Jonsson拟变种及其Jonsson谱
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-12-30 DOI: 10.31489/2022m4/117-124
A. Yeshkeyev, I.O. Tungushbayeva, S.M. Amanbekov
{"title":"Existentially prime Jonsson quasivarieties and their Jonsson spectra","authors":"A. Yeshkeyev, I.O. Tungushbayeva, S.M. Amanbekov","doi":"10.31489/2022m4/117-124","DOIUrl":"https://doi.org/10.31489/2022m4/117-124","url":null,"abstract":"This article is devoted to the study of Jonsson quasivarieties in a signature enriched with new predicate and constant symbols. New concepts of semantic Jonsson quasivariety and fragment-conservativeness of the center of the Jonsson theory are introduced. The cosemanticness classes of the Jonsson spectrum constructed for a semantic Jonsson quasvariety are considered. In this case, the Kaiser hull of the semantic Jonsson quasivariety is assumed to be existentially prime. By constructing a central type for classes of theories from the Jonsson spectrum, the following results are formulated and proved. In the first main result, the necessary and sufficient condition is given for the center of the cosemanticness class of an existentially prime semantic Jonsson quasivariety to be λ-stable. The second result is the criterion for the center of the class of theories to be ω-categorical in the enriched language. The obtained theorems can be useful in continuing studies of various Jonsson algebras, in particular, Jonsson quasivarieties.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46460444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the approximation of solutions of one singular differential equation on the axis 关于一个奇异微分方程在轴上解的近似
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-12-30 DOI: 10.31489/2022m/86-97
A. S. Kassym, L. Kussainova
{"title":"On the approximation of solutions of one singular differential equation on the axis","authors":"A. S. Kassym, L. Kussainova","doi":"10.31489/2022m/86-97","DOIUrl":"https://doi.org/10.31489/2022m/86-97","url":null,"abstract":"In this paper we study the problem of the best approximation by linear methods of solutions to one Triebel-type equation. This problem was solved by using estimates of the linear widths of the unit ball in corresponding spaces of differentiable functions. According to the definition, linear widths give the best estimates for the approximation of compact sets in a given normed space by linear methods which are implemented through finite-dimensional operators. The problem includes answers to the questions about the solvability of the studied equation, the construction of the corresponding weighted space of differentiable functions, the development of a method for estimating linear widths of compact sets in weighted polynomial Sobolev space. In this work, conditions are obtained under which the considered operator has a bounded inverse. The weighted Sobolev space corresponding to the posed problem is determined. Upper estimates are obtained for the counting function for a sequence of linear widths, which correspond to the posed problem. One example is constructed in which two-sided estimates of linear widths are given. The method for solving this problem can be applied to the numerical solution of non-standard ordinary differential equations on an infinite axis.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41855951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The theorems about traces and extensions for functions from Nikolsky-Besov spaces with generalized mixed smoothness 具有广义混合光滑性的Nikolsky Besov空间中函数的迹和扩张定理
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-12-30 DOI: 10.31489/2022m4/42-50
K. Bekmaganbetov, K.Ye. Kervenev, Y. Toleugazy
{"title":"The theorems about traces and extensions for functions from Nikolsky-Besov spaces with generalized mixed smoothness","authors":"K. Bekmaganbetov, K.Ye. Kervenev, Y. Toleugazy","doi":"10.31489/2022m4/42-50","DOIUrl":"https://doi.org/10.31489/2022m4/42-50","url":null,"abstract":"The theory of embedding of spaces of differentiable functions studies important relations of differential (smoothness) properties of functions in various metrics and has wide application in the theory of boundary value problems of mathematical physics, approximation theory and other fields of mathematics. In this article, we prove the theorems about traces and extensions for functions from Nikolsky-Besov spaces with generalized mixed smoothness and mixed metrics. The proofs of the obtained results is based on the inequality of different dimensions for trigonometric polynomials in Lebesgue spaces with mixed metrics and the embedding theorem of classical Nikolsky-Besov spaces in the space of continuous functions.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49620423","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On bounded solutions of linear systems of differential equations with unbounded coefficients 系数无界的线性微分方程组的有界解
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-12-30 DOI: 10.31489/2022m4/107-116
R.Ye. Uteshova, Ye.V. Kokotova
{"title":"On bounded solutions of linear systems of differential equations with unbounded coefficients","authors":"R.Ye. Uteshova, Ye.V. Kokotova","doi":"10.31489/2022m4/107-116","DOIUrl":"https://doi.org/10.31489/2022m4/107-116","url":null,"abstract":"This paper deals with a problem of finding a bounded solution of a system of nonhomogeneous linear differential equations with an unbounded matrix of coefficients on a finite interval. The right-hand side of the equation belongs to a space of continuous functions bounded with some weight; the weight function is chosen taking into account the behavior of the coefficient matrix. The problem is studied using a modified version of the parameterization method with non-uniform partitioning. Necessary and sufficient conditions of well-posedness of the problem are obtained in terms of a bilaterally infinite matrix of special structure.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42078558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Inverse coefficient problem for differential equation in partial derivatives of a fourth order in time with integral over-determination 具有积分过定的四阶时间偏导数微分方程的反系数问题
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-12-30 DOI: 10.31489/2022m4/51-59
M. J. Huntul, I. Tekin
{"title":"Inverse coefficient problem for differential equation in partial derivatives of a fourth order in time with integral over-determination","authors":"M. J. Huntul, I. Tekin","doi":"10.31489/2022m4/51-59","DOIUrl":"https://doi.org/10.31489/2022m4/51-59","url":null,"abstract":"Derivatives in time of higher order (more than two) arise in various fields such as acoustics, medical ultrasound, viscoelasticity and thermoelasticity. The inverse problems for higher order derivatives in time equations connected with recovery of the coefficient are scarce and need additional consideration. In this article the inverse problem of determination is considered which depends on time, lowest term coefficient in differential equation in partial derivatives of fourth order in time with initial and boundary conditions from an additional integral observation is considered. Under some conditions regularity, consistency and orthogonality of data by using of the contraction principle the unique solvability of the solution of the coefficient identification problem on a sufficiently small time interval has been proved.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41600175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Systems of integral equations with a degenerate kernel and an algorithm for their solution using the Maple program 退化核积分方程组及其Maple程序求解算法
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-12-30 DOI: 10.31489/2022m4/60-75
B. Kalimbetov, V. Safonov, O. D. Tuychiev
{"title":"Systems of integral equations with a degenerate kernel and an algorithm for their solution using the Maple program","authors":"B. Kalimbetov, V. Safonov, O. D. Tuychiev","doi":"10.31489/2022m4/60-75","DOIUrl":"https://doi.org/10.31489/2022m4/60-75","url":null,"abstract":"In the mathematical literature, a scalar integral equation with a degenerate kernel is well described (see below (1)), where all the written functions are scalar quantities). The authors are not aware of publications where systems of integral equations of (1) type with kernels in the form of a product of matrices would be considered in detail. It is usually said that the technique for solving such systems is easily transferred from the scalar case to the vector one (for example, in the monograph A.L. Kalashnikov \"Methods for the approximate solution of integral equations of the second kind\" (Nizhny Novgorod: Nizhny Novgorod State University, 2017), a brief description of systems of equations with degenerate kernels is given, where the role of degenerate kernels is played by products of scalar rather than matrix functions). However, as the simplest examples show, the generalization of the ideas of the scalar case to the case of integral systems with kernels in the form of a sum of products of matrix functions is rather unclear, although in this case the idea of reducing an integral equation to an algebraic system is also used. At the same time, the process of obtaining the conditions for the solvability of an integral system in the form of orthogonality conditions, based on the conditions for the solvability of the corresponding algebraic system, as it seems to us, has not been previously described. Bearing in mind the wide applications of the theory of integral equations in applied problems, the authors considered it necessary to give a detailed scheme for solving integral systems with degenerate kernels in the multidimensional case and to implement this scheme in the Maple program. Note that only scalar integral equations are solved in Maple using the intsolve procedure. The authors did not find a similar procedure for solving systems of integral equations, so they developed their own procedure.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43836448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the convergence of difference schemes of high accuracy for the equation of ion-acoustic waves in a magnetized plasma 磁化等离子体中离子声波方程高精度差分格式的收敛性
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2022-12-30 DOI: 10.31489/2022m4/4-19
M. Aripov, D. Utebaev, Zhusipbay Nurullaev
{"title":"On the convergence of difference schemes of high accuracy for the equation of ion-acoustic waves in a magnetized plasma","authors":"M. Aripov, D. Utebaev, Zhusipbay Nurullaev","doi":"10.31489/2022m4/4-19","DOIUrl":"https://doi.org/10.31489/2022m4/4-19","url":null,"abstract":"Multiparametric difference schemes of the finite element method of a high order of accuracy for the Sobolevtype equation of the fourth-order in time are studied. In particular, the first boundary value problem for the equation of ion-acoustic waves in a magnetized plasma is considered. A high-order accuracy of the scheme is achieved due to the special discretization of time and space variables. The presence of parameters in the scheme makes it possible to regularize the accuracy of the schemes and optimize the implementation algorithm. An a priori estimate in a weak norm is obtained by the method of energy inequality. Based on this estimate and the Bramble-Hilbert lemma, the convergence of the constructed algorithms in classes of generalized solutions is proved. An algorithm for implementing the difference scheme is proposed.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48604123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信